Combustion detecting method of engine

ABSTRACT

A combustion phase detection method of an engine has the advantages of being able to reduce exhaust gas and to improve combustion stability, to compensate injection and ignition delay time between combustion chambers and between cycles, and to detect a combustion phase in real time such that a heat generation rate and heat release can be effectively calculated in an early state of combustion with a simple calculation method to control combustion of an engine, by using a combustion pressure and a motoring pressure difference of an engine not affected by an offset value of the cylinder pressure. For this, a combustion phase detection method may include detecting a combustion phase by using a specific point of DRdV as follows: 
     
       
         
           
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     Here, the Pdiff (P−Pmotoring) is a difference between a cylinder measure combust pressure (P) and a motoring pressure (Pmotoring), and V is a combustion chamber volume.

CROSS-REFERENCE TO RELATED APPLICATION

This application claims priority to and the benefit of Korean PatentApplication No. 10-2010-0094890 filed Sep. 30, 2010, the entire contentsof which application is incorporated herein for all purposes by thisreference.

BACKGROUND OF INVENTION

1. Field of Invention

The present invention relates to a combustion phase detection methodthat uses a volume change rate and a pressure of a combustion chamber.

2. Description of Related Art

In an internal combustion engine, an abnormal combustion process, forexample, knocking, can be generated by spontaneous combustion of anunburned mixture that a fire does not yet reach. Long continued knockingcan damage components of the combustion chamber by an increment of heatload and pressure shock.

An important parameter that affects a knocking tendency of the internalcombustion engine is ignition timing. If the fuel/air mixture in thecombustion chamber is ignited too early, the knocking can be generated.Accordingly, after a knocking process is detected in the internalcombustion engine, there is a method that retards ignition timing so asto prevent the knocking at a next combustion stroke.

Excessively retarded ignition is related to efficiency loss, andaccordingly a knocking control apparatus is used to detect knockingduring combustion in the internal combustion engine. This part ofknocking control is knocking detection. Meanwhile, the ignition angle isadjusted during knocking control. Knocking control like this ispublished in an international patent application PCT/DE 91/00170. Otheradjustment parameters such as fuel/air mixture, charging, compressionratio, an engine operating point, and so on can be varied so as toreduce knocking sensitivity of the internal combustion engine.

Also, knocking control is separately performed for each cylinder, and inaddition to knocking detection, separately adjusting an ignition anglefor each cylinder has been published. Since a structure difference of acylinder, inequitable distribution of knocking sensors, and a relatedknocking signal of a cylinder generate differences of cylinders inknocking control, a separate knocking control for each cylinder is to beused to optimize efficiency thereof and simultaneously knockingsensitivity is deteriorated thereby.

If the phase detection portion, in which signals based onsynchronization of ignition and knocking control are transferred, breaksdown, a new demand condition is given to the knocking control that isseparately performed for each cylinder. The knocking control isperformed with maximum security and maximum accuracy so as to achievemaximum efficiency, due to possible damage of the internal combustionengine and stability of the combustion.

On this account, the necessity for the combustion phase control shows asteady growth to achieve stability of the combustion and noxious exhaustgas reduction.

Generally, the combustion phase control method includes calculatingtotal heat release (referring to a total heat release of FIG. 1) byusing the following Equation 1 and a pressure inside the combustionchamber, and detecting a combustion phase by using a specific point ofthe total heat release (for example, 50% of the total heat release, MFB50: 0.5 value of axis y coordinate of FIG. 1).

$\begin{matrix}{\frac{\mathbb{d}Q}{\mathbb{d}\theta} = {{\frac{1}{\gamma - 1}V\frac{\mathbb{d}P}{\mathbb{d}\theta}} + {\frac{\gamma}{\gamma - 1}P\frac{\mathbb{d}V}{\mathbb{d}\theta}}}} & {{Eq}.\mspace{14mu} 1}\end{matrix}$

However, since the above heat generation analysis method is based on athermal dynamics rule and it is very complicated mathematically and hasa large size of calculation load, it is effective in a case that it isanalyzed at a theoretical side with sufficient time, but there is adrawback that it is difficult to apply it to the combustion of theengine that is performed in real time.

Also, in the combustion phase detection method that uses a 50% point ofthe heat generation (MFB 50), as shown in FIG. 2, there was a problemthat a larger error is generated in detecting the combustion phase, in acase that an offset is formed in a sensor measure value by heat impactwhen the cylinder combustion pressure is measured, as shown in a squarepattern mark coordinator of FIG. 3, compared to a normal circle markcoordinator.

The information disclosed in this Background section is only forenhancement of understanding of the general background of the inventionand should not be taken as an acknowledgement or any form of suggestionthat this information forms the prior art already known to a personskilled in the art.

SUMMARY OF INVENTION

Various aspects of the present invention provide for a combustion phasedetection method of an engine having advantages of being able to reduceexhaust gas and to improve combustion stability, to compensate injectionand ignition delay time between combustion chambers and between cycles,and to detect a combustion phase in real time such that a heatgeneration rate and heat release can be effectively calculated in anearly state of combustion with a simple calculation method to controlcombustion of an engine, by using a combustion pressure and a motoringpressure difference of an engine not affected by an offset value of thecylinder pressure.

One aspect of the present invention is directed to a combustion phasedetection method may include detecting a combustion phase by using aspecific point of DRdV through a following equation

${DR}{\mathbb{d}V}\text{:}\mspace{14mu}\frac{P_{diff}\frac{\mathbb{d}V}{\mathbb{d}\theta}}{\max\left( {P_{diff}\frac{\mathbb{d}V}{\mathbb{d}\theta}} \right)}$

Here, Pdiff (P−Pmotoring) is a difference between a cylinder measurecombust pressure (P) and a motoring pressure (Pmotoring), and V is acombustion chamber volume.

The specific point for detecting the combustion phase may be within DRdV0-50% and is within 0-20° based on a crank angle.

The specific point for detecting the combustion phase may be DRdV 50%and a crank angle 20°.

A normalization method of the DRdV may include calculating by applying amotoring pressure and a pressure difference that is formed by acombustion instead of a cylinder measure pressure P in a conventionalheat release, calculating an approximate heat release value by ignoringa heat release rate by the motoring pressure having a very small amount,and normalizing, as illustrated by the following equations:

$\frac{\mathbb{d}Q}{\mathbb{d}\theta} = {{\frac{1}{\gamma - 1}V\frac{\mathbb{d}P}{\mathbb{d}\theta}} + {\frac{\gamma}{\gamma - 1}P\frac{\mathbb{d}V}{\mathbb{d}\theta}}}$${\frac{\mathbb{d}Q}{\mathbb{d}\theta} = {{\frac{1}{\gamma - 1}V\frac{\mathbb{d}\left( {P_{diff} + P_{motoring}} \right)}{\mathbb{d}\theta}} + {\frac{\gamma}{\gamma - 1}\left( {P_{diff} + P_{motoring}} \right)\frac{\mathbb{d}V}{\mathbb{d}\theta}}}},{{{where}\mspace{14mu} P_{diff}} = {P - P_{motoring}}}$$\frac{\mathbb{d}Q}{\mathbb{d}\theta} = {{\frac{1}{\gamma - 1}\left( {{V\frac{\mathbb{d}P_{diff}}{\mathbb{d}\theta}} + {\gamma\; P_{diff}\frac{\mathbb{d}V}{\mathbb{d}\theta}}} \right)} + {\frac{1}{\gamma - 1}\left( {{V\frac{\mathbb{d}P_{motoring}}{\mathbb{d}\theta}} + {\gamma\; P_{motoring}\frac{\mathbb{d}V}{\mathbb{d}\theta}}} \right)}}$$\frac{\mathbb{d}Q}{\mathbb{d}\theta} \simeq {\frac{1}{\gamma - 1}{\left( {{V\frac{\mathbb{d}P_{diff}}{\mathbb{d}\theta}} + {\gamma\; P_{diff}\frac{\mathbb{d}V}{\mathbb{d}\theta}}} \right).}}$

Other aspects of the present invention are directed to an incipientcombustion heat generation rate detection method and combustion phasedetection method in which an incipient heat generation rate can bedetected through a small amount of calculation, compared to aconventional heat generation rate detection method, and a combustionphase can be detected in real time by using a specific point of anincipient heat generation rate. This can be effectively applied to acombustion phase control system such that injection and ignition delaytime between combustion chambers or between cycles is compensated, theexhaust gas is reduced, and the combustion stability is improved.

The methods and apparatuses of the present invention have other featuresand advantages which will be apparent from or are set forth in moredetail in the accompanying drawings, which are incorporated herein, andthe following Detailed Description, which together serve to explaincertain principles of the present invention.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a graph showing conventional total heat release forcontrolling a combustion phase.

FIG. 2 shows that many errors are generated in a combustion phase, incase an offset is generated in a sensor measure value by heat impactwhen a cylinder combustion pressure is measured, wherein the upper curveis a normal cylinder pressure and the lower curve is a cylinder pressurein a case of an offset.

FIG. 3 shows a result of a combustion phase detection, which uses a 50%point of heat release (e.g., 50% of fuel mass burned or MFB50), whereinan upper end square mark is a combustion phase when a cylinder pressureoffset occurs, and a lower end circle mark is an MFB50 of a normalcondition to show that there is an error as large as a height differencebetween both sides in combustion phase detection.

FIG. 4 is a combustion pressure and motoring pressure graph.

FIG. 5 is a graph that compares DRdV as heat release of the presentinvention with a conventional heat release.

FIG. 6 is a graph showing a relationship between a crank angle and anormalized value of DRdV of the present invention.

FIG. 7 is a graph showing a 40% point of DRdV, which is normalized,according to fuel injection timing of the present invention.

DETAILED DESCRIPTION

Reference will now be made in detail to various embodiments of thepresent invention(s), examples of which are illustrated in theaccompanying drawings and described below. While the invention(s) willbe described in conjunction with exemplary embodiments, it will beunderstood that present description is not intended to limit theinvention(s) to those exemplary embodiments. On the contrary, theinvention(s) is/are intended to cover not only the exemplaryembodiments, but also various alternatives, modifications, equivalentsand other embodiments, which may be included within the spirit and scopeof the invention as defined by the appended claims.

A conventional fuel injection system uses feed-forward control. However,in spite of an equal fuel injection order, in a case that fuel injectionis controlled by feed-forward control, the injection and the ignitioncan be delayed according to driving conditions of an engine such thatthe combustion phase is varied. Since the variation of the combustionphase increases exhaust gas or decreases combustion stability, thecombustion phase is to be accurately controlled by feedback control.

For this, a conventional combustion phase detection method forcontrolling a combustion phase detects a combustion phase by using aspecific point of heat release (for example, 50% of fuel mass burned, orMFB50), but it may cause an error of the combustion phase when an offsetis generated by the cylinder pressure sensor and a calculation load ishigh such that real time control is hard to realize.

Given this point, because a difference of the combustion pressure andthe motoring pressure are used in the present invention, it is notaffected by an offset of the cylinder pressure, and a calculation loadthereof is low in contrast to the conventional method to estimate a heatgeneration rate and a heat release at an early stage of the combustionwith ease, and the method will be described hereafter.

The following Equation 1 is used to calculate a heat generation rate, aconventional cylinder measure combustion pressure P minus pressure(Pmotoring) is a pressure difference (Pdiff) that is generated bycombustion to effectively control combustion, i.e. Pdiff=P−Pmotoring orP=Pdiff+Pmotoring, Pdiff+Pmotoring is applied instead of P in aconventional equation, and the heat generation rate of Equation 2according to the present invention can be received.

$\begin{matrix}{\frac{\mathbb{d}Q}{\mathbb{d}\theta} = {{\frac{1}{\gamma - 1}V\frac{\mathbb{d}P}{\mathbb{d}\theta}} + {\frac{\gamma}{\gamma - 1}P\frac{\mathbb{d}V}{\mathbb{d}\theta}}}} & {{Equation}\mspace{14mu} 1} \\{{\frac{\mathbb{d}Q}{\mathbb{d}\theta} = {{\frac{1}{\gamma - 1}V\frac{\mathbb{d}\left( {P_{diff} + P_{motoring}} \right)}{\mathbb{d}\theta}} + {\frac{\gamma}{\gamma - 1}\left( {P_{diff} + P_{motoring}} \right)\frac{\mathbb{d}V}{\mathbb{d}\theta}}}},{{{where}\mspace{14mu} P_{diff}} = {P - P_{motoring}}}} & {{Equation}\mspace{14mu} 2}\end{matrix}$

The above Equation 2 is arranged to be transformed to a followingEquation 3.

$\begin{matrix}{\frac{\mathbb{d}Q}{\mathbb{d}\theta} = {{\frac{1}{\gamma - 1}\left( {{V\frac{\mathbb{d}P_{diff}}{\mathbb{d}\theta}} + {\gamma\; P_{diff}\frac{\mathbb{d}V}{\mathbb{d}\theta}}} \right)} + {\frac{1}{\gamma - 1}\left( {{V\frac{\mathbb{d}P_{motoring}}{\mathbb{d}\theta}} + {\gamma\; P_{motoring}\frac{\mathbb{d}V}{\mathbb{d}\theta}}} \right)}}} & {{Equation}\mspace{14mu} 3}\end{matrix}$

However, the heat generation rate by the motoring pressure is a valuethat can be omitted in Equation 3, and resultantly the heat generationrate can be expressed as the following Equation 4 as an approximatevalue.

$\begin{matrix}{\frac{\mathbb{d}Q}{\mathbb{d}\theta} \simeq {\frac{1}{\gamma - 1}\left( {{V\frac{\mathbb{d}P_{diff}}{\mathbb{d}\theta}} + {\gamma\; P_{diff}\frac{\mathbb{d}V}{\mathbb{d}\theta}}} \right)}} & {{Equation}\mspace{14mu} 4}\end{matrix}$

Next, γ/γ−1*Pdiff dV/dθ of the Equation 4 is normalized by a followingEquation 5 (hereinafter, this normalized value or “normalized heatrelease” is DRdV (Difference pressure rate of heat release using dVterm)), and a characteristic of the DRdV is used to detect a combustionphase according to a fuel injection.

$\begin{matrix}{{DR}{\mathbb{d}V}\text{:}\mspace{14mu}\frac{P_{diff}\frac{\mathbb{d}V}{\mathbb{d}\theta}}{\max\left( {P_{diff}\frac{\mathbb{d}V}{\mathbb{d}\theta}} \right)}} & {{Equation}\mspace{14mu} 5}\end{matrix}$

Hereinafter, the calculation method will be further described withreference to accompanying drawings.

FIG. 1 is a graph showing a result of total heat release that iscalculated by detecting a combustion pressure inside a combustionchamber and substituting the detected pressure into Equation 1. This isa conventional method for combustion phase control, wherein a specificpoint of the total heat release (for example, 0.5 of axis y, that is a50% point) is used to detect a combustion phase, but this ismathematically very complicated and a calculation load thereof is highas described above and therefore it is hard to apply this method in realtime.

Also, as shown in FIG. 2, in a case that an offset is generated in ameasured value of a sensor by a heat impact when a cylinder combustionpressure is measured, a larger error is formed in a combustion phase.The upper curve is a normal cylinder combustion pressure, the lowercurve is a cylinder pressure in an offset case, and a difference betweenboth curved lines is an error.

FIG. 3 shows a result of combustion phase detection, which uses a 50%point of heat release (for example, 50% fuel mass burned, or MFB50),wherein an upper end square mark is a combustion phase when a cylinderpressure offset occurs, and a lower end circle mark is an MFB50 of anormal condition to show that there is an error as large as a heightdifference between both sides in combustion phase detection.

FIG. 4 is a combustion pressure and motoring pressure graph, wherein acylinder combustion pressure curve and a motoring pressure curvecoincide at the left side of a peak point, and there is a littledifference therebetween at the right side thereof.

FIG. 5 is a graph showing a relation between a conventional heat releaseand a DRdV that is heat release of the present invention, this graphcompares a normalized heat release (DRdV) that is calculated byintegrating γ/γ−1*Pdiff dV/dθ of the Equation 4 through the Equation 5with a normalized heat release that is calculated by integrating aconventional Equation 1.

As shown in the FIG. 5, while the combustion is performed, the DRdV anda conventional heat release is almost the same characteristic (i.e.,both curved lines almost coincide) until the heat release reaches 50%(around 0.5 of Axis y, crank angle 20° of Axis x), wherein if thecharacteristic of the DRdV according to the present invention is used,the combustion phase according to the fuel injection is accurately andsimply detected.

FIG. 6 is a DRdV graph of the present invention, if a specific point(this is marked as DRdVx, for example, 50% point denotes DRdV50, and 75%point denotes DRdV75) of the DRdV is used, the combustion phase can bedetected, the detected value is usefully used in the combustion phasecontrol, for one example, FIG. 7 shows a 75% point (DRdV75) of DRdVaccording to a fuel injection timing, wherein it can be confirmed that acombustion phase is varied according to a variation of a fuel injectiontiming.

While this invention has been described in connection with what ispresently considered to be practical exemplary embodiments, it is to beunderstood that the invention is not limited to the disclosedembodiments, but, on the contrary, is intended to cover variousmodifications and equivalent arrangements included within the spirit andscope of the appended claims.

For convenience in explanation and accurate definition in the appendedclaims, the terms upper or lower, and etc. are used to describe featuresof the exemplary embodiments with reference to the positions of suchfeatures as displayed in the figures.

The foregoing descriptions of specific exemplary embodiments of thepresent invention have been presented for purposes of illustration anddescription. They are not intended to be exhaustive or to limit theinvention to the precise forms disclosed, and obviously manymodifications and variations are possible in light of the aboveteachings. The exemplary embodiments were chosen and described in orderto explain certain principles of the invention and their practicalapplication, to thereby enable others skilled in the art to make andutilize various exemplary embodiments of the present invention, as wellas various alternatives and modifications thereof. It is intended thatthe scope of the invention be defined by the Claims appended hereto andtheir equivalents.

What is claimed is:
 1. A combustion phase detection method, comprising:determining, by an engine control unit (ECU), a pressure difference(Pdiff) between a cylinder measure combust pressure (P) and a motoringpressure (Pmotoring), wherein Pdiff=P−Pmotoring; calculating, by theECU, a specific point of a normalized heat release (DRdV) through thefollowing equation${DR}{\mathbb{d}V}\text{:}\mspace{14mu}\frac{P_{diff}\frac{\mathbb{d}V}{\mathbb{d}\theta}}{\max\left( {P_{diff}\frac{\mathbb{d}V}{\mathbb{d}\theta}} \right)}$wherein V is a combustion chamber volume; and detecting, by the ECU, acombustion phase based on the calculated specific point of DRdV.
 2. Thecombustion phase detection method of claim 1, wherein the specific pointfor detecting the combustion phase is within DRdV 0-50% and is within acrank angle of 0-20°.
 3. The combustion phase detection method of claim1, wherein the normalized heat release is divided into a before-peakarea and an after-peak area, whereby the before-peak area is related toa first-half stage of combustion (DRdV 0-50%) and the after-peak area isrelated to a second-half stage of combustion (DRdV 51-100%).
 4. Thecombustion phase detection method of claim 2, wherein the specific pointfor detecting the combustion phase is DRdV 50% and a crank angle 20°. 5.The combustion phase detection method of claim 1, wherein anormalization method of the DRdV includes: $\begin{matrix}{\frac{\mathbb{d}Q}{\mathbb{d}\theta} = {{\frac{1}{\gamma - 1}V\frac{\mathbb{d}P}{\mathbb{d}\theta}} + {\frac{\gamma}{\gamma - 1}P\frac{\mathbb{d}V}{\mathbb{d}\theta}}}} & {{Equation}\mspace{14mu} 1} \\{{\frac{\mathbb{d}Q}{\mathbb{d}\theta} = {{\frac{1}{\gamma - 1}V\frac{\mathbb{d}\left( {P_{diff} + P_{motoring}} \right)}{\mathbb{d}\theta}} + {\frac{\gamma}{\gamma - 1}\left( {P_{diff} + P_{motoring}} \right)\frac{\mathbb{d}V}{\mathbb{d}\theta}}}},{{{where}\mspace{14mu} P_{diff}} = {P - P_{motoring}}}} & {{Equation}\mspace{14mu} 2} \\{\frac{\mathbb{d}Q}{\mathbb{d}\theta} = {{\frac{1}{\gamma - 1}\left( {{V\frac{\mathbb{d}P_{diff}}{\mathbb{d}\theta}} + {\gamma\; P_{diff}\frac{\mathbb{d}V}{\mathbb{d}\theta}}} \right)} + {\frac{1}{\gamma - 1}\left( {{V\frac{\mathbb{d}P_{motoring}}{\mathbb{d}\theta}} + {\gamma\; P_{motoring}\frac{\mathbb{d}V}{\mathbb{d}\theta}}} \right)}}} & {{Equation}\mspace{14mu} 3} \\{\frac{\mathbb{d}Q}{\mathbb{d}\theta} \simeq {\frac{1}{\gamma - 1}\left( {{V\frac{\mathbb{d}P_{diff}}{\mathbb{d}\theta}} + {\gamma\; P_{diff}\frac{\mathbb{d}V}{\mathbb{d}\theta}}} \right)}} & {{Equation}\mspace{14mu} 4}\end{matrix}$ calculating Equation 2 and Equation 3 by applying amotoring pressure and a pressure difference that is formed by acombustion instead of a cylinder measure pressure P in the aboveheat-release Equation 1: calculating Equation 4 as an approximate heatrelease value by ignoring a heat release rate by the motoring pressurehaving a very small amount in the above Equation 3; and normalizing theequation of claim 1 by using the above Equation
 4. 6. A combustion phasedetection system, comprising an engine that uses a combustion energy togenerate power; and an ECU that detects a combustion timing, and thatperforms: determining a pressure difference (Pdiff) between a cylindermeasure combust pressure (P) and a motoring pressure (Pmotoring),wherein Pdiff=P−Pmotoring; and calculating a specific point of anormalized heat release (DRdV) through the following equation${DR}{\mathbb{d}V}\text{:}\mspace{14mu}\frac{P_{diff}\frac{\mathbb{d}V}{\mathbb{d}\theta}}{\max\left( {P_{diff}\frac{\mathbb{d}V}{\mathbb{d}\theta}} \right)}$wherein the Pdiff (P−Pmotoring) is a difference between a cylindermeasure combust pressure (P) and a motoring pressure (Pmotoring), and Vis a combustion chamber volume; and detecting a combustion phase basedon the calculated specific point of DRdV.
 7. The combustion phasedetection system of claim 6, wherein the specific point for detectingthe combustion phase is within DRdV 0-50% and is within a crank angle of0-20°.
 8. The combustion phase detection method of claim 6, wherein thenormalized heat release is divided into a before-peak area and anafter-peak area, whereby the before-peak area is related to a first-halfstage of combustion (DRdV 0-50%) and the after-peak area is related to asecond-half stage of combustion (DRdV 51-100%).
 9. The combustion phasedetection system of claim 7, wherein the specific point for detectingthe combustion phase is DRdV 50% and a crank angle 20°.
 10. Thecombustion phase detection system of claim 6, wherein the ECU performs anormalization method of the DRdV including: $\begin{matrix}{\frac{\mathbb{d}Q}{\mathbb{d}\theta} = {{\frac{1}{\gamma - 1}V\frac{\mathbb{d}P}{\mathbb{d}\theta}} + {\frac{\gamma}{\gamma - 1}P\frac{\mathbb{d}V}{\mathbb{d}\theta}}}} & {{Equation}\mspace{14mu} 1} \\{{\frac{\mathbb{d}Q}{\mathbb{d}\theta} = {{\frac{1}{\gamma - 1}V\frac{\mathbb{d}\left( {P_{diff} + P_{motoring}} \right)}{\mathbb{d}\theta}} + {\frac{\gamma}{\gamma - 1}\left( {P_{diff} + P_{motoring}} \right)\frac{\mathbb{d}V}{\mathbb{d}\theta}}}},{{{where}\mspace{14mu} P_{diff}} = {P - P_{motoring}}}} & {{Equation}\mspace{14mu} 2} \\{\frac{\mathbb{d}Q}{\mathbb{d}\theta} = {{\frac{1}{\gamma - 1}\left( {{V\frac{\mathbb{d}P_{diff}}{\mathbb{d}\theta}} + {\gamma\; P_{diff}\frac{\mathbb{d}V}{\mathbb{d}\theta}}} \right)} + {\frac{1}{\gamma - 1}\left( {{V\frac{\mathbb{d}P_{motoring}}{\mathbb{d}\theta}} + {\gamma\; P_{motoring}\frac{\mathbb{d}V}{\mathbb{d}\theta}}} \right)}}} & {{Equation}\mspace{14mu} 3} \\{\frac{\mathbb{d}Q}{\mathbb{d}\theta} \simeq {\frac{1}{\gamma - 1}\left( {{V\frac{\mathbb{d}P_{diff}}{\mathbb{d}\theta}} + {\gamma\; P_{diff}\frac{\mathbb{d}V}{\mathbb{d}\theta}}} \right)}} & {{Equation}\mspace{14mu} 4}\end{matrix}$ means for calculating Equations 2 and 3 by applying amotoring pressure and a pressure difference that is formed by acombustion instead of a cylinder measure pressure P in the above heatrelease Equation 1; means for calculating Equation 4 as an approximateheat release value by ignoring a heat release rate by the motoringpressure having a very small amount in Equation 3; and means fornormalizing the equation of claim 5 using the above Equation 4.